Undergrad Why is there no consensus about the meaning of probability in MWI?

[PeterDonis]

MWI goes to great lengths to contruct a set of equiprobable, orthonormal, "microstates" for that purpose.

Does it? I understand that MWI proponents claim this. But where in the math are these "microstates"? There are amplitudes for each term in the wave function, but amplitudes are not states.

 

[kered rettop]

Edit: funny enough the difference between interpretations is not sharp, it even leads to bold claims like MWI= Bohmian mechanics or MWI=superdeterminism

I've heard of Bohmiam mechanics being called "MWI in denial" but why on earth would anyone say "MWI=superdeterminism"?

 

[jbergman]

Does it? I understand that MWI proponents claim this. But where in the math are these "microstates"? There are amplitudes for each term in the wave function, but amplitudes are not states.

I believe they assume there other states that you can tensor product with what you are observing to give you a much larger number of total worlds.

 

[kered rettop]

Does it? I understand that MWI proponents claim this. But where in the math are these "microstates"?

I dont know what you mean by "where in the maths".

There are amplitudes for each term in the wave function, but amplitudes are not states.

True, but why say so? I do not understand your point at all.

 

[gentzen]

I've heard of Bohmiam mechanics being called "MWI in denial" but why on earth would anyone say "MWI=superdeterminism"?

Probably because he misunderstands superdeterminism. Historically, the name "superdeterminism" arose when somebody (I can lookup who it was) pointed out a tricky loophole in Bell's theorem. Bell admitted the existence of that loophole, but tried to dismiss it nevertheless by badmouthing it. I had always admiration for people like Jarek Duda that came up with proposals like maximal entropy random walk, which "accidentally" violated the superderminism loophole.

 

[kered rettop]

I believe they assume there other states that you can tensor product with what you are observing to give you a much larger number of total worlds.

I believe that too. I also believe that, even if they mean something completely different - like "mushrooms talk in the dark", it would still have been a correct assumption. The tensor product one, not the mushroom one.

 

[PeterDonis]

I dont know what you mean by "where in the maths".

I mean just what I say. If I make a spin measurement on a qubit with, say, probability 2/3 for one outcome and 1/3 for the other, the math says there are two outcomes with unequal weights. It does not say there are 3 outcomes, two of which happen to be identical. At least, that's the math I'm aware of. So for anyone who wants to claim there are in fact 3 outcomes, I am asking what math they are using and where in that math the 3 outcomes are, because I don't see them in any math I'm aware of; I only see two outcomes.

why say so?

See above.

 

[pines-demon]

Jarek Duda that came up with proposals like maximal entropy random walk, which "accidentally" violated the superderminism loophole.

Please tell, what is this about?

 

[PeterDonis]

I believe they assume there other states that you can tensor product with what you are observing to give you a much larger number of total worlds.

What states? Where do they come from? And how can it possibly be legitimate to just assume they are there, instead of actually doing the math and showing that they are there?

 

[kered rettop]

Please tell, what is this about?

Well it certainly isn't about the topic of the thread. Which I started because I wanted to know. (I still don't.) Maybe everyone thinks it's been done to death and are now throwing snowballs at each other to relax?

 

[gentzen]

Please tell, what is this about?

Just a concrete example why "superdeterminism" should just means to violate that tricky loophole in Bell's theorem. Of course, it does points to a certain kind of defect, like an effective violation of the arrow of time. But maybe you still can get something good or interesting in exchange for that defect.

 

[pines-demon]

Just a concrete example why "superdeterminism" should just means to violate that tricky loophole in Bell's theorem. Of course, it does points to a certain kind of defect, like an effective violation of the arrow of time. But maybe you still can get something good or interesting in exchange for that defect.

I do not want to get too far from the topic. But so Duda came up with a classical stochastic system that violates statistical independence?

Sorry @kered rettop I will go back to topic soon.

 

[PeterDonis]

the topic of the thread. Which I started because I wanted to know. (I still don't.)

Well, the thread's title question, if not quite answered to your satisfaction, is certainly illustrated by the discussion we've had, in which no consensus has been achieved.

 

[kered rettop]

I mean just what I say. If I make a spin measurement on a qubit with, say, probability 2/3 for one outcome and 1/3 for the other, the math says there are two outcomes with unequal weights. It does not say there are 3 outcomes, two of which happen to be identical. At least, that's the math I'm aware of. So for anyone who wants to claim there are in fact 3 outcomes, I am asking what math they are using and where in that math the 3 outcomes are, because I don't see them in any math I'm aware of; I only see two outcomes.

Well, you've switched to talking about outcomes of the initial measurement. I was talking about the product terms when you do a fine-grained decomposition of the decohered state. (Down to every degree of freedom if necessary.) Is not such a term a state?

 

[kered rettop]

Well, the thread's title question, if not quite answered to your satisfaction, is certainly illustrated by the discussion we've had, in which no consensus has been achieved.

True. But I never doubted the lack of consensus.
Anyway, I still want to digest your post #18 so I'm not giving up on the thread yet.

 

[kered rettop]

Sorry @kered rettop I will go back to topic soon.

Don't bother, nobody else does!

 

[PeterDonis]

you've switched to talking about outcomes of the initial measurement.

No, I haven't "switched" (but see further comment at the end of this post). The different decohered outcomes are the "worlds" in the MWI. So those are the relevant things to be looking at.

I was talking about the product terms when you do a fine-grained decomposition of the decohered state. (Down to every degree of freedom if necessary.) Is not such a term a state?

They aren't "worlds" in MWI-speak. If decoherence spreads entanglement through, say, $10^{30}$ degrees of freedom in the environment after I measure the spin of a qubit, that doesn't mean the number of "worlds" goes from $2$ (one for each outcome) to $10^{30}$. It's still just $2$ worlds.

At some point the term "state" appears to have entered the discussion, but unless it is taken to be a synonym for "world" in MWI-speak, I'm not sure what relevance it has. If I am partly responsible for the inadvertent switch in terminology, I apologize.

 

[Demystifier]

There is no collapse for Bohmians.

Can you provide some source to show that Bohmians derive the Born rule? Where is the house Bohmian @Demystifier ?

There is no true fundamental collapse, but there is effective apparent collapse, Bohmian mechanics explains it in a rather simple way. It explains easily the Born rule in arbitrary space (momentum, energy, spin etc. space) from the Born rule in position space, see e.g. my https://arxiv.org/abs/1811.11643 . For the explanation of the Born rule in position space itself, see https://www.mdpi.com/1099-4300/20/6/422 .

 

[PeroK]

Here is explicitly how a probabilistic model can be simulated by a deterministic model.

Take $2^{33}$ people, each in a sealed room. That's approx the current Earth population, so it seemed a good number to choose.

In the probability model, pick one of them. Toss a coin 33 times on their behalf and give them the string of heads and tails.

In the simulated model go through all possibilities for strings of 33 heads or tails and give each one to someone. In this model, every person has a different string ranging from 33 heads to 33 tails and everything in between.

The point is that each person in the simulated model cannot tell which experiment is being done. Likewise, the person in the probability model above, cannot tell which experiment they are part of.

In particular, the person with 33 heads and the one with 33 tails cannot conclude they are in the simulation.

This, in terms of probability theory is clear. There should be no argument that probabilities can be simulated in this way.

 

[PeterDonis]

In particular, the person with 33 heads and the one with 33 tails cannot conclude they are in the simulation.

Why not?

 

[PeroK]

Why not?

For the same reason that the person in probability scenario cannot conclude they are in the simulation. They were subject to the unlikely one in $2^{33}$ probability of being chosen.

 

[PeterDonis]

For the same reason that the person in probability scenario cannot conclude they are in the simulation. They were subject to the unlikely one in $2^{33}$ probability of being chosen.

Sorry, I don't see the connection here. Every person in the experiment knows that there is only one person in the probability scenario, while there are $2^{33}$ people in the simulation (i.e., all of them). So each person would conclude that it is overwhelmingly likely that they are in the simulation, even before seeing the data they are given. Seeing 33 heads or 33 tails just makes it even more overwhelmingly likely that they are in the simulation, since in the simulation it is guaranteed that someone will see those data sets, whereas in the probability scenario they are overwhelmingly unlikely.

 

[PeterDonis]

For the same reason that the person in probability scenario cannot conclude they are in the simulation.

And also cannot conclude that they are not, correct? You said they can't know which experiment they are part of.

But what is the reason for that? It is because the data set the person in the probability scenario will see will be one that doesn't give them any useful information about which scenario they are in. Since every data set occurs in the simulation, the only data sets that don't give any useful information about which scenario one is in are data sets that are likely to occur in the probability scenario. A data set that is overwhelmingly unlikely to occur in the probability scenario, like the ones with 33 heads and 33 tails, does give useful information about which scenario one is in, since such data sets are not unlikely to occur in the simulation--they can't be, because they are guaranteed to occur in the simulation.

 

[PeroK]

Sorry, I don't see the connection here. Every person in the experiment knows that there is only one person in the probability scenario, while there are $2^{33}$ people in the simulation (i.e., all of them). So each person would conclude that it is overwhelmingly likely that they are in the simulation, even before seeing the data they are given. Seeing 33 heads or 33 tails just makes it even more overwhelmingly likely that they are in the simulation, since in the simulation it is guaranteed that someone will see those data sets, whereas in the probability scenario they are overwhelmingly unlikely.

It's true that in this thought experiment everyone can guess they are in the simulation. Knowledge of the other people is a flaw in how I've set it up. I'm sure that can be fixed.

 

[PeterDonis]

It's true that in this thought experiment everyone can guess they are in the simulation. Knowledge of the other people is a flaw in how I've set it up. I'm sure that can be fixed.

If you're sure, then please fix it. I'm not at all sure it can be fixed. You are struggling with an issue that MWI proponents have been struggling with for a number of decades now, and IMO none of them has fixed it. The basic problem, as I said, is that in the MWI all possible outcomes are guaranteed to occur. Nobody has come up with a meaningful concept of probability in that context, and it's not for lack of trying.

 

[PeroK]

If you're sure, then please fix it. I'm not at all sure it can be fixed. You are struggling with an issue that MWI proponents have been struggling with for a number of decades now, and IMO none of them has fixed it. The basic problem, as I said, is that in the MWI all possible outcomes are guaranteed to occur. Nobody has come up with a meaningful concept of probability in that context, and it's not for lack of trying.

They have the problem of extending it beyond the simple equally likely scenarios. There may be some deeper issues even there.

 

[pines-demon]

If you're sure, then please fix it. I'm not at all sure it can be fixed. You are struggling with an issue that MWI proponents have been struggling with for a number of decades now, and IMO none of them has fixed it. The basic problem, as I said, is that in the MWI all possible outcomes are guaranteed to occur. Nobody has come up with a meaningful concept of probability in that context, and it's not for lack of trying.

Just remove the knowledge that there is other people doing the experiment....

Why is so bad that some people get impossibly unlikely odds? Quantum suicide and all that, these are very exceptional cases and these observers will not able to derive the right probabilities, but the more coins throws and people you add the less exceptional cases there are relative to the majority. There is consensus in MWI that these exceptional cases must exist but are not important.

 

[Fra]

As there appears to be no consensus about the meaning of probability in a deterministic model, I am asking what the sticking point is?
That's all really.

fwif, I rarely engage in mwi discussions, but if I were to make a comment to your original question, from another (agent/qbist centered view) I would like to describe it like this.

To give both descriptive or normative probabilities a real meaning we need to have an observer or agent that is either collecting and processing the data to infer the descriptive probability(statistics) in some limit, or an agent that uses his incomplete knowledge to place bets.

Mwi attempt to do away with obsevers, is to me like denying that observers are real physical systems, and to say that "any possibility" always occurs, is to suggest that all possible physical observers actually exist. This makes no sense to me. Everything that is possible, does not necessarily actually happen, especially if you take the normative interpretation of probability.

But one you start to think about this, which I have done, mwi seems not interesting to me at least.

A similar situation can appear in a agent-centered kind of "solipsist" view, where you can argue that there is always some "strange agent" that can have a particular biased inferred normative view of the future. BUT the thind is that if you take seriously that agents/observers are not just fictions but real objects (having mass!) and not just a "coordinate system" that is fictive, then it seems reasonable that the population of agents in the universe is not arbitrary, therefore, everyone that seems possible, in a remote future, does not actually happen.

/Fredrik

 

[pines-demon]

fwif, I rarely engage in mwi discussions, but if I were to make a comment to your original question, from another (agent/qbist centered view) I would like to describe it like this.

To give both descriptive or normative probabilities a real meaning we need to have an observer or agent that is either collecting and processing the data to infer the descriptive probability(statistics) in some limit, or an agent that uses his incomplete knowledge to place bets.

Mwi attempt to do away with obsevers, is to me like denying that observers are real physical systems, and to say that "any possibility" always occurs, is to suggest that all possible physical observers actually exist. This makes no sense to me. Everything that is possible, does not necessarily actually happen, especially if you take the normative interpretation of probability.

But one you start to think about this, which I have done, mwi seems not interesting to me at least.

A similar situation can appear in a agent-centered kind of "solipsist" view, where you can argue that there is always some "strange agent" that can have a particular biased inferred normative view of the future. BUT the thind is that if you take seriously that agents/observers are not just fictions but real objects (having mass!) and not just a "coordinate system" that is fictive, then it seems reasonable that the population of agents in the universe is not arbitrary, therefore, everyone that seems possible, in a remote future, does not actually happen.

/Fredrik

Everything, that is consequence of a quantum superposition, happens according to MWI. Why the observer cannot be the one at the end of each branch? Do you agree that if you accept that there are strange agents, then the probability could be defined?

 

[kered rettop]

They have the problem of extending it beyond the simple equally likely scenarios. There may be some deeper issues even there.

No they don't. MWI does not calculate probabilities the way you suggest. It never counts the number of outcomes to calculate probabilies. There is nothing to extend.